Various display devices for displaying images have been developed. For example, a head-mounted display (hereinafter referred to as “HMD”) is exemplified as these display devices.
A user wears the HMD on the head. The HMD displays an image in front of the eyes of the user to provide the user with information. In general, it is desired in terms of wearability that the HMD is small and lightweight.
A conventional HMD includes a small liquid crystal panel and an optical magnifier (e.g. a convex lens or a free curve prism). The magnifier magnifies an image to be displayed by the liquid crystal panel. Accordingly, a magnified virtual image is observed by a user (c.f. Patent Document 1). In the following description, display techniques for magnifying an image using the magnifier is referred to as “optical magnification system”.
A display device with a computer generated hologram (hereinafter referred to as “CGH”) is exemplified as another display technique (c.f. Patent Document 2). For example, the display device includes a light source, a liquid crystal panel of a phase modulation type, and a computer for creating a computer generated hologram. When image data is input to the computer, the computer calculates a diffraction pattern. The display device displays the diffraction pattern on the liquid crystal panel as the CGH. When the light source emits a laser beam to the liquid crystal panel, a wave front of display light is reproduced from a virtual image position. Accordingly, a user may observe a virtual image.
Unlike the optical magnification system, the display technique using the CGH does not require a magnifier such as a prism. Therefore, if the CGH is used, it is possible to design a small optical system. Accordingly, a small HMD may be manufactured under use of the CGH.
(Image Display Method Using CGH)
FIG. 24A is an exemplary image represented by image data input to the computer. FIG. 24B is an exemplary diffraction pattern in correspondence to the image data shown in FIG. 24A. An image display method using a CGH is described with reference to FIGS. 24A and 24B.
The display device using the CGH calculates a diffraction pattern from the image data. Image generation techniques using a point filling method or Fourier transform are exemplified as calculation techniques for the diffraction pattern. For example, the display device may generate the diffraction pattern shown in FIG. 24B from the image data representing the image shown in FIG. 24A. The display device displays the generated diffraction pattern on the liquid crystal panel (e.g. a phase modulation type) as the CGH. When the display device irradiates a laser beam on the liquid crystal panel which displays the CGH, the liquid crystal panel diffracts the laser beam according to the diffraction pattern. Accordingly, a user may observe the diffracted laser beam as the image shown in FIG. 24A.
(Generation Method for Diffraction Pattern)
FIG. 25 is a conceptual view of a generation method for a diffraction pattern according to the point filling method. The generation method for a diffraction pattern is described with reference to FIG. 25.
FIG. 25 shows an image represented by image data and a ξ-η coordinate set on the liquid crystal panel. The origin of the ξ-η coordinate is coincident with the center of the liquid crystal panel.
If the point filling method is used, the image represented by the image data is regarded as a set of point light sources. In FIG. 25, a point i on the image is shown. A diffraction pattern is calculated from a phase at the time when emission light emitted from a point on the image overlaps a point on the liquid crystal panel.
The following formula represents a complex amplitude ui (ξ,η) of light which reaches a point u from the point i.
                              ui          ⁡                      (                          ξ              ,              η                        )                          =                                            α              ⁢                                                          ⁢              i                        ri                    ⁢          exp          ⁢                      {                          -                              j                ⁡                                  (                                      kri                    +                                          ϕ                      ⁢                                                                                          ⁢                      i                                                        )                                                      }                                              [                  Formula          ⁢                                          ⁢          1                ]            
It should be noted that the symbol “αi” in the aforementioned formula represents amplitude of light at the point i. The symbol “φi” represents a phase of the light at the point i. It should be noted that the phase “φi” may be a random phase value added to the image The symbol “k” represents a wave number. If a wavelength of light emitted from the point i is represented by the symbol “λ”, the wave number “k” is represented by “2π/λ”. The symbol “ri” represents a distance between the point i and the point u. The distance “ri” is represented by the following formula.ri=√{square root over ((ξ−xi)2+(η−yi)2+zi2)}  [Formula 2]
It should be noted that the coordinate of the point i is represented by (xi, yi, zi) in the aforementioned formula. The coordinate of the point u is represented by (ξ, η, 0).
Complex amplitude of light reaching the point u from each of all points on the image is represented as a sum of complex amplitudes of lights reaching the point u from the points on the image. The following formula represents the complex amplitude of the light reaching the point u from each of all the points on the image.
                              u          ⁡                      (                          ξ              ,              η                        )                          =                              ∑                          i              =              1                        N                    ⁢                                          ⁢                      ui            ⁡                          (                              ξ                ,                η                            )                                                          [                  Formula          ⁢                                          ⁢          3                ]            
The calculation of the aforementioned formula is executed on all points on the liquid crystal panel. Accordingly, a diffraction pattern is generated. It should be noted that a phase change resultant from reference light is not shown in the calculation according to the point filling method, in order to simplify description about the principle of the point filling method.
As described above, if the diffraction pattern is calculated by means of the point filling method, a wave front from an arbitrary object is reproduced. Therefore, unlike the conventional optical magnification system, a position of a reproduced image which a user observes is appropriately controlled without a magnifier such as a prism.
(Problem about Angle of View)
The display device using the CGH faces a problem about a small angle of view of a reproduced image.
FIG. 26 shows the liquid crystal panel, illumination light for illuminating the liquid crystal panel, and diffracted light which is diffracted by the liquid crystal panel. The problem about the angle of view is described with reference to FIG. 26.
The liquid crystal panel shown in FIG. 26 displays a CGH. When the illumination light is irradiated on the liquid crystal panel, the liquid crystal panel generates diffracted light in correspondence to the CGH. It should be noted that the CGH generates several kinds of diffracted light different in orders. However, only primary diffracted light is shown in FIG. 26.
The following formula represents an angle between the diffracted light and a perpendicular line of the liquid crystal panel (i.e. an angle of diffraction θa). It should be noted that a pixel pitch of the liquid crystal display panel is represented by the symbol “p”. A wavelength of the illumination light is represented by the symbol “λ”.
                              θ          ⁢                                          ⁢          a                =                  λ                      2            ⁢                                                  ⁢            p                                              [                  Formula          ⁢                                          ⁢          4                ]            
It is figured out from the aforementioned formula that the small pixel pitch “p” results in the large angle of diffraction θa. In general, if a diffractable range of the diffracted light from the liquid crystal panel is large, an angle of view and a vision of a reproduced image are easily magnified. However, it is difficult to create a pixel pitch smaller than 6 μm according to current manufacturing techniques for liquid crystal panels. In short, there is a limit in obtaining a large angle of diffraction θa by using the pixel pitch.
The illumination light shown in FIG. 26 is collimated light perpendicular to the liquid crystal panel. Unlike the techniques shown in FIG. 26, Patent Document 3 proposes to change an incident angle of the illumination light irradiated on the liquid crystal panel in order to obtain a large angle of diffraction.
FIG. 27 shows setting techniques for an angle of diffraction proposed by Patent Document 3. The setting techniques for an angle of diffraction proposed by Patent Document 3 are described with reference to FIGS. 26 and 27.
Like FIG. 26, FIG. 27 shows diffracted light, which is inclined by an angle “θa” from the perpendicular line of the liquid crystal panel. Unlike FIG. 26, the illumination light is inclined by an angle “θb” from the perpendicular line of the liquid crystal panel. In this case, the liquid crystal panel diffracts the illumination light by an angle “θc” equivalent to a difference between the angles “θa” and “θb”. If the illumination light is inclined from the perpendicular line of the liquid crystal panel, an angle of diffraction required for the liquid crystal panel decreases. Therefore, a wide angle of view is obtained by using a factor different from the pixel pitch.
The setting techniques for an angle of diffraction described with reference to FIG. 27 are easily realized by using convergent light as the illumination light. However, if the convergent light is used as the illumination light, a large optical system is required.
FIG. 28 is a schematic view of an optical system 900 configured to generate convergent light. The optical system 900 is described with reference to FIG. 28.
The optical system 900 includes a light source 910, a condensing lens 920 and a liquid crystal panel 930. The light source 910 emits emission light EML. The emission light EML is divergent light. The condensing lens 920 changes the emission light EML to convergent light CVL. The convergent light CVL enters the liquid crystal panel 930. The liquid crystal panel 930 displays a CGH. Therefore, the liquid crystal panel 930 diffracts the convergent light CVL to generate diffracted light DFL.
FIG. 29 is a schematic view showing a relationship of sizes between the condensing lens 920 and the liquid crystal panel 930. The relationship of sizes between the condensing lens 920 and the liquid crystal panel 930 is described with reference to FIG. 29.
A diameter of the condensing lens 920 is represented by the symbol “W”. A diameter of the liquid crystal panel 930 is represented by the symbol “D”. The convergent light CVL is inclined by an angle “θb” from the perpendicular line NL to the liquid crystal panel 930. A distance between the condensing lens 920 and the liquid crystal panel 930 is represented by the symbol “L”. The following formula represents the diameter “W” of the condensing lens 920.W=2×L×tan θb+D  [Formula 5]
As described above, an increase in the angle “θb” of the convergent light CVL may be considered as a method of increasing an angle of diffraction. However, it is figured out from the aforementioned formula that the large angle “θb” results in the large diameter “W” of the condensing lens 920. The long distance between the condensing lens 920 and the liquid crystal panel 930 also results in the large diameter “W” of the condensing lens 920. It is figured out from these optical perceptions that the conventional techniques are likely to require a large optical system. However, the large optical system is unsuitable for an application to a wearable display device such as an HMD in terms of an external appearance.
Patent Document 1: JP H8-240773 A
Patent Document 2: JP 2008-541145 A
Patent Document 3: JP 2011-35899 A